Please help important!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Mathematics

2 answers:

qwelly [4]3 years ago

8 0

Answer:

Step-by-step explanation:

Alexeev081 [22]3 years ago

6 0

Answer:

Step-by-step explanation:

The initial fee of $12 would be the y-intercept because no matter how many boxes of cards you buy, the fee stays the same. The slope would be $3.99 because that fee is charged per box. The 100 cards per box is extra information and not needed in the equation. D is the only logical choice.

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skad [1K]

Parameterize S by the vector function

$\vec s(u,v) = \left\langle 4 \cos(u) \sin(v), 4 \sin(u) \sin(v), 4 \cos(v) \right\rangle$

with 0 ≤ u ≤ π/2 and 0 ≤ v ≤ π/2.

Compute the outward-pointing normal vector to S :

$\vec n = \dfrac{\partial\vec s}{\partial v} \times \dfrac{\partial \vec s}{\partial u} = \left\langle 16 \cos(u) \sin^2(v), 16 \sin(u) \sin^2(v), 16 \cos(v) \sin(v) \right\rangle$

The integral of the field over S is then

$\displaystyle \iint_S \vec f \cdot d\vec s = \int_0^{\frac\pi2} \int_0^{\frac\pi2} \vec f(\vec s) \cdot \vec n \, du \, dv$

$\displaystyle = \int_0^{\frac\pi2} \int_0^{\frac\pi2} \left\langle 8 \cos(u) \sin(v), -12 \cos(v), 12 \sin(u) \sin(v) \right\rangle \cdot \vec n \, du \, dv$